AI 中文总结
研究大气建模中输运主导流动的数值稳定方法，通过在特定软件包中实现SU和SUPG公式，与其他方法比较，发现准单调限制器能最小化非物理极值，SUPG在保留特征和结构方面最佳，还分析了SUPG性质并提出算法。
AI 中文摘要
本报告探讨并比较了大气建模中输运主导流动的数值稳定方法。在Julia的this http URL包和Python的Firedrake包中，针对带开槽圆柱初始条件的测试问题，实现了流线迎风（SU）和流线迎风彼得罗夫-伽辽金（SUPG）稳定公式。将这些方法与现有的超扩散和准单调限制器方法及其各种组合进行比较，以评估它们减轻虚假振荡同时保留尖锐特征的能力。对于该基准测试，准单调限制器在最小化非物理极值方面最有效，但代价是扩散整体结构。在计算误差指标方面，对于此测试案例，未发现SUPG方法比无稳定情况有所改进。然而，在测试的稳定运行中，它在保留尖锐特征和整体结构方面表现最佳。分析了SUPG的理论性质，并提出了基于渐近分析的SUPG算法作为未来工作。
英文摘要
This report explores and compares numerical stabilization methods for transport-dominated flows arising in atmospheric modeling. The Streamline-Upwind (SU) and Streamline-Upwind Petrov-Galerkin (SUPG) stabilization formulations are implemented in Julia's ClimaCore.jl package and Python's Firedrake package for a test problem with slotted-cylinder initial conditions. These methods are compared for their ability to mitigate spurious oscillations while preserving sharp features against existing hyperdiffusion and quasi-monotone limiter methods, alongside various combinations. For this benchmark, quasi-monotone limiters were most effective at minimizing un-physical extrema, at the expense of diffusing the overall structure. The SUPG method was not found to improve upon the no stabilization case, for this test case in the computed error metrics. However, it performs best at preserving sharp feature and overall structure, among tested stabilized runs. Theoretical properties of SUPG are analyzed, and an asymptotics-based SUPG algorithm is proposed as future work.
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